Question 89
Prove that among any four numbers from the interval $\langle 0, \frac{\pi}{2} \rangle$ one can choose two numbers, namely $x$ and $y$, such that
$$
8 \cos x \cos y \cos(x - y) + 1 \gt 4 (\cos^2 x + \cos^2 y).
$$
$$
8 \cos x \cos y \cos(x - y) + 1 \gt 4 (\cos^2 x + \cos^2 y).
$$